Average Error: 0.1 → 0.1
Time: 12.4s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)
double f(double x) {
        double r164102 = 841.0;
        double r164103 = 108.0;
        double r164104 = r164102 / r164103;
        double r164105 = x;
        double r164106 = r164104 * r164105;
        double r164107 = 4.0;
        double r164108 = 29.0;
        double r164109 = r164107 / r164108;
        double r164110 = r164106 + r164109;
        return r164110;
}
↓
double f(double x) {
        double r164111 = 841.0;
        double r164112 = 108.0;
        double r164113 = r164111 / r164112;
        double r164114 = x;
        double r164115 = 4.0;
        double r164116 = 29.0;
        double r164117 = r164115 / r164116;
        double r164118 = fma(r164113, r164114, r164117);
        return r164118;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))